Gravitational interactions with information dynamics

Introduction Unifying gravity with quantum mechanics remains a cornerstone challenge in physics, with information theory providing a transformative perspective through concepts like the holographic principle and entropic gravity. Methods We derive an observer-independent information density field from coarse-grained Shannon entropy of classical matter configurations at nuclear scales, establish thermodynamically motivated coupling constants using hadronic physics, prove gauge invariance including novel information symmetries, and enhance experimental designs with detailed error budgets and theory differentiation. Results The framework predicts modified gravitational lensing corrections <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>δ</mml:mi><mml:mo>∼</mml:mo><mml:mn>1</mml:mn><mml:msup><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>8</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> and quantum phase shifts ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m2"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>ϕ</mml:mi><mml:mo>∼</mml:mo><mml:mn>1</mml:mn><mml:msup><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>12</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math> rad), verifiable within 1–5 years using precision astrometry and matter-wave interferometry, supported by comprehensive derivations, Python verification code, and professional diagrams. Discussion This work positions information-theoretic gravity as a rigorous, testable paradigm that bridges classical relativity and quantum information, with potential extensions to broader unification while maintaining focus on gravitational interactions.